In this paper, we shall demonstrate the efficiency of this mechanism for a concrete and well-motivated source of high-scale \(CP\)  violation: axion inflation coupled to the SM hypercharge sector [1]}, [2]}, [3]}, [4]}, which spontaneously breaks \(CP\)  invariance by means of the nonzero and time-dependent value of the axion inflaton field during inflation.
Axion inflation coupled to gauge fields has been extensively studied in the literature and gives rise to a rich phenomenology.
In the version of the model that we are interested in, the violation of \(CP\)  invariance is communicated to the Standard Model via the axion–vector coupling \(\phi Y_{\mu \nu }\widetilde{Y}^{\mu \nu }\) , where \(\phi \)  is the axion inflaton field, \(Y_{\mu \nu }\)  is the hypercharge field strength tensor, and \(\widetilde{Y}^{\mu \nu }\)  denotes its dual.
This coupling results in the generation of helical hypermagnetic fields (i.e., primordial hypermagnetogenesis) [5]}, [6]}, [7]}, which in turn leads to the nonperturbative production of SM fermions via the Schwinger effect [8]}, [9]}, [10]}.
The fermionic charge asymmetries generated during inflation are dictated by the SM chiral anomaly [11]}, [12]} and set the initial conditions for the chemical transport after inflation.
At the same time, the helicity stored in the hypermagnetic field is approximately conserved, as long as processes such as magnetic diffusion [13]}, [14]}, [15]} and the chiral plasma instability (CPI) [16]}, [17]}, [18]}, [19]}, [20]}, [21]}, [22]} can be neglected.
If it survives all the way down to the EWPT, its decay around the time of sphaleron freeze-out yields another relevant contribution to the BAU [23]}, [24]}, [25]}, [22]}, in addition to the leptogenesis contribution generated at higher temperatures.
Following up on Ref. [27]}, the aim of the present paper is to provide a unified description of these different mechanisms.
